I think that the prime universe should be left alone in terms of TV shows - leave it to games and stuff to continue that part. I see parallels with Stargate - the technology is just too powerful now, one of the galaxy's big villains seem much of a threat and simply introducting yet another just seems wrong (Stargate Universe tried something different, but that didn't turn out well). A reboot of both is best, imo.
After a few films set in the new universe, I'd like a new TV series set 70-80 years after the films (around the same time as TNG) so they have a lot of leeway in how things are (butterfly effect). They could make it very different - completely different crew, perhaps a ship design nothing like the Galaxy. It would be nice to have one or two characters the same (like Guinan turning up in an episode, one of the main cast or recurring characters turning up, etc). It would also be nice to have one two-parter involving the Temporal Cold War (perhaps with even Bakula making an appearance) and even one or two episodes which have a similar plot to TNG.
But, ultimately, it would be a brand new mythos with similar building blocks. Much less canon to try and comply to and a bigger empty space for much more creativity.